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A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.
In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime [nb 1] that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space.
Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime.. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.
A category for 4-vectors, (and closely related 4-operators) which are mathematical objects used in the special theory of relativity. Pages in category "Four-vectors" The following 11 pages are in this category, out of 11 total.
Therefore, in thermo-mechanical situations the time component of the four-force is not proportional to the power but has a more generic expression, to be given case by case, which represents the supply of internal energy from the combination of work and heat, [2] [1] [4] [3] and which in the Newtonian limit becomes +.
The 4-divergence of this current is: = + where ∂ μ is the 4-gradient and μ is an index labeling the spacetime dimension. Then the continuity equation is: ∂ μ J μ = 0 {\displaystyle \partial _{\mu }J^{\mu }=0} in the usual case where there are no sources or sinks, that is, for perfectly conserved quantities like energy or charge.
In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity).
State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. One of the more popular reference frames for the state vectors of bodies moving near Earth is the Earth-centered inertial (ECI) system defined as follows: [1]: 23 The origin is Earth's center of mass;